Quadratic Functions and Equations in Financial Context — Quiz Answers

An investor has $⁢190,000 to distribute between two investments. The risk function is R⁡(x)=0.035⁢x^2−0.062⁢x+0.031 If x is the portion invested in the first option, how much should the investor put into the second investment to minimize risk? Round to the nearest hundredth if necessary.

To anticipate future returns on earnings, a business owner starts by finding the break-even point of a new product. The revenue function is R⁡(x)=−0.0096⁢x^2+600⁢x , and the cost function is C⁡(x)=185,000+480⁢x In both functions, x is the number of units sold. According to the functions, what is the larger number of units the company can sell to break even? Round your answer to the nearest thousand. Enter your answer in the box.

An investor has $⁢215,000 to distribute between two investments. Let x be the portion invested in the first option. How much should the investor put into the first investment option to minimize risk if the risk function is R⁡(x)=0.055⁢x^2−0.096⁢x+0.048 ? Round your answer to the nearest thousand. Enter your answer in the box.

The price that companies set for a product is determined by market demand. The equation graph, where x is the number of units, represents the demand. For how many units is the demand 0 ? Round to the nearest whole number. Expand Image Enter your answer in the box.

An investor is trying to minimize risk when distributing funds between two investments. The risk function is R⁡(x)=0.0802⁢x^2−0.0722⁢x+0.0361 If x is the portion invested in the first option, how should the investor distribute the funds to minimize risk?

An investor wants to minimize risk by distributing funds into two options. The risk function is R⁡(x)=0.061⁢x^2−1.058⁢x+0.529 If x is the portion invested in the first option, how should the investor distribute the funds to minimize risk?

A shares transaction summary shows a total cost of $⁢2,400 before fees. If the share price had been $⁢2 cheaper, the investor could have purchased 200 more shares. Simplify and factor the equation (2,400)/(x−2)−(2,400)/(x)=200 to find the price per share of the stock. Round to the nearest hundredth if necessary.

The profit formula for a company can be represented using the function P⁡(x)=−6⁢x^2+2,400⁢x−12,000 , where x is the selling price of the product. An investor will purchase stock shares when the profits are predicted to be greater than $⁢189,600 Complete the range of selling prices for which the profits will meet the investor's requirements. Round to the nearest cent if necessary. Enter your answers in the boxes.

To determine whether to purchase a company's stock, an investor will use a profit-prediction formula for a company's signature product depending on that product’s current selling price. The profit formula for the company can be represented using the function P⁡(x)=−20⁢x^2+4,400⁢x−24,000 , where x is the selling price of the product. Use a graphing calculator to determine the selling price that results in the maximum profits. Round to the nearest cent if necessary.

For a new product that will be released nationwide, the revenue function is R⁡(x)=−0.007⁢x^2+18,125⁢x and the cost function is C⁡(x)=428,000+13,532⁢x In both functions, x is the number of units produced. How many units does the company need to sell to break even? Round your answer to the nearest thousand.

To determine whether to purchase a company's stock, an investor will use a profit-prediction formula for a company's signature product depending on that product’s current selling price. The profit formula for the company can be represented using the function P⁡(x)=−20⁢x^2+4,400⁢x−24,000 , where x is the selling price of the product. Use a graphing calculator to determine the selling price that results in the maximum profits. Round to the nearest cent if necessary.

An investor has $⁢60,000 to distribute between two investments. Let x be the portion invested in the first option. How much should the investor put into the first investment option to minimize risk if the risk function is R⁡(x)=0.019⁢x^2−0.034⁢x+0.017 ? Round your answer to the nearest hundred. Enter your answer in the box.

To determine whether a company’s profits will justify purchasing its stock, an investor wants to know the maximum possible profits for the company's signature product. The profit formula for the signature product can be represented using the function P⁡(x)=−7⁢x^2+4,200⁢x−20,000 , where x is the selling price of the product. What numbers for the selling price and the projected profit at the maximum of the function can the investor use to determine whether purchasing the stock is viable? Round to the nearest cent if necessary. Enter your answer in the boxes.

An investor has $⁢12,000 to distribute between two investments. If x is the portion invested in the first option, how should the investor distribute the funds to minimize the risk if the risk function is R⁡(x)=0.046⁢x^2−0.068⁢x+0.034 ? Give the answers as decimals to the nearest thousandth. Enter your answers in the boxes.

An investor has $⁢215,000 to distribute between two investments. Let x be the portion invested in the first option. How much should the investor put into the first investment option to minimize risk if the risk function is R⁡(x)=0.055⁢x^2−0.096⁢x+0.048 ? Round your answer to the nearest thousand. Enter your answer in the box.

An investor has $⁢12,000 to distribute between two investments. If x is the portion invested in the first option, how should the investor distribute the funds to minimize the risk if the risk function is R⁡(x)=0.046⁢x^2−0.068⁢x+0.034 ? Give the answers as decimals to the nearest thousandth. Enter your answers in the boxes.

A shares transaction summary shows a total purchase price of $⁢8,743.80 before fees. If the share price had been $⁢0.20 cheaper, the investor could have purchased 35 more shares. Simplify the equation (8,743.50)/(x−0.2)−(8,734.8)/(x)=35 and use the quadratic formula to find the price per share of the stock. Round to the nearest hundredth if necessary.

An investor has $⁢12,000 to distribute between two investments. If x is the portion invested in the first option, how should the investor distribute the funds to minimize the risk if the risk function is R⁡(x)=0.046⁢x^2−0.068⁢x+0.034 ? Give the answers as decimals to the nearest thousandth. Enter your answers in the boxes.

To anticipate future returns on earnings, a business owner starts by finding the break-even point of a new product. The revenue function is R⁡(x)=−0.0096⁢x^2+600⁢x , and the cost function is C⁡(x)=185,000+480⁢x In both functions, x is the number of units sold. According to the functions, what is the larger number of units the company can sell to break even? Round your answer to the nearest thousand. Enter your answer in the box.

A shares transaction summary shows a total cost of $⁢2,400 before fees. If the share price had been $⁢2 cheaper, the investor could have purchased 200 more shares. Simplify and factor the equation (2,400)/(x−2)−(2,400)/(x)=200 to find the price per share of the stock. Round to the nearest hundredth if necessary.